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The rating algorithm was updated starting 2021. The whole database from back in 1996 was recalculated with this algorithm. You can find the old algorithm here.

Ratings are updated by: r' = r + con * (Sa - Se) + bonus
r is the old EGD rating (GoR) of the player
r' is the new EGD rating of the player
Sa is the actual game result (1.0 = win, 0.5 = jigo, 0.0 = loss)
Se is the expected game result as a winning probability (1.0 = 100%, 0.5 = 50%, 0.0 = 0%). See further below for its computation.
con is a factor that determines rating volatility (similar to K in regular Elo rating systems): con = ((3300 - r) / 200) ^ 1.6
bonus (not found in regular Elo rating systems) is a term included to counter rating deflation: bonus = ln(1 + exp((2300 - rating) / 80)) / 5
Se is computed by the Bradley-Terry formula: Se = 1 / (1 + exp(β(r2) - β(r1)))
r1 is the EGD rating of the player
r2 is the EGD rating of the opponent
β is a mapping function for EGD ratings: β = -7 * ln(3300 - r)

EGF Official ratings system

Usage

composer require horaceho/ers

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Horaceho\Ers;

$ers = new Ers\Ers();

$player = 2100.0;
$opponent = 2100.0;
$win = 1.0;
$loss = 0.0;

$win_update = $ers->update($player, $opponent, $win);
assert ($win_update == 2109.306);
echo $win_update . PHP_EOL;

Test

git clone git@github.com:horaceho/ers.git
cd ers
php test/ers.php
php test/about.php

horaceho / ers

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